Tapan Mukerji

The Rock Physics Handbook: Contents

Responding to the latest developments in rock physics research, this popular reference book has been thoroughly updated while retaining its comprehensive coverage of the fundamental theory, concepts, and laboratory results. It brings together the vast literature from the field to address the relationships between geophysical observations and the underlying physical properties of Earth materials - including water, hydrocarbons, gases, minerals, rocks, ice, magma and methane hydrates. This third edition includes expanded coverage of topics such as effective medium models, viscoelasticity, attenuation, anisotropy, electrical-elastic cross relations, and highlights applications in unconventional reservoirs. Appendices have been enhanced with new materials and properties, while worked examples (supplemented by online datasets and MATLAB® codes) enable readers to implement the workflows and models in practice. This significantly revised edition will continue to be the go-to reference for students and researchers interested in rock physics, near-surface geophysics, seismology, and professionals in the oil and gas industries.

The Rock Physics Handbook by Gary Mavko

Responding to the latest developments in rock physics research, this popular reference book has been thoroughly updated while retaining its comprehensive coverage of the fundamental theory, concepts, and laboratory results. It brings together the vast literature from the field to address the relationships between geophysical observations and the underlying physical properties of Earth materials - including water, hydrocarbons, gases, minerals, rocks, ice, magma and methane hydrates. This third edition includes expanded coverage of topics such as effective medium models, viscoelasticity, attenuation, anisotropy, electrical-elastic cross relations, and highlights applications in unconventional reservoirs. Appendices have been enhanced with new materials and properties, while worked examples (supplemented by online datasets and MATLAB® codes) enable readers to implement the workflows and models in practice. This significantly revised edition will continue to be the go-to reference for students and researchers interested in rock physics, near-surface geophysics, seismology, and professionals in the oil and gas industries.

Bounds on low‐frequency seismic velocities in partially saturated rocks

The most common technique for estimating seismic velocities in rocks with mixed pore fluid saturations is to use Gassmann’s relations with an effective fluid whose density and compressibility are averages of the individual pore fluid properties. This approach is applicable only if the gas, oil, and brine phases are mixed uniformly at a very small scale, so the different wave‐induced increments of pore pressure in each phase have time to diffuse and equilibrate during a seismic period. In contrast, saturations that are heterogeneous over scales larger than the characteristic diffusion length, i.e., patchy saturation, will always lead to higher seismic velocities than if the same fluids are mixed uniformly at a fine scale. Critical saturation scales separating uniform from patchy behavior are typically of the order 0.1–1 cm for laboratory measurements and tens of centimeters for field seismic frequencies. For low seismic frequencies, velocities corresponding to patchy and homogeneous saturations represent a...

Digital rock physics benchmarks-part II: Computing effective properties

This is the second and final part of our digital rock physics (DRP) benchmarking study. We use segmented 3-D images (one for Fontainebleau, three for Berea, three for a carbonate, and one for a sphere pack) to directly compute the absolute permeability, the electrical resistivity, and elastic moduli. The numerical methods tested include a finite-element solver (elastic moduli and electrical conductivity), two finite-difference solvers (elastic moduli and electrical conductivity), a Fourier-based Lippmann-Schwinger solver (elastic moduli), a lattice-Boltzmann solver (hydraulic permeability), and the explicit-jump method (hydraulic permeability and electrical conductivity). The set-ups for these numerical experiments, including the boundary conditions and the total model size, varied as well. The results thus produced vary from each other. For example, the highest computed permeability value may differ from the lowest one by a factor of 1.5. Nevertheless, all these results fall within the ranges consistent with the relevant laboratory data. Our analysis provides the DRP community with a range of possible outcomes which can be expected depending on the solver and its setup.

Seismic inversion for reservoir properties combining statistical rock physics and geostatistics: A review

There are various approaches for quantitative estimation of reservoir properties from seismic inversion. A general Bayesian formulation for the inverse problem can be implemented in two different work flows. In the sequential approach, first seismic data are inverted, deterministically or stochastically, into elastic properties; then rock-physics models transform those elastic properties to the reservoir property of interest. The joint or simultaneous work flow accounts for the elastic parameters and the reservoir properties, often in a Bayesian formulation, guaranteeing consistency between the elastic and reservoir properties. Rock physics plays the important role of linking elastic parameters such as impedances and velocities to reservoir properties of interest such as lithologies, porosity, and pore fluids. Geostatistical methods help add constraints of spatial correlation, conditioning to different kinds of data and incorporating subseismic scales of heterogeneities.

Mapping lithofacies and pore-fluid probabilities in a North Sea reservoir: Seismic inversions and statistical rock physics

Reliably predicting lithologic and saturation heterogeneities is one of the key problems in reservoir characterization. In this study, we show how statistical rock physics techniques combined with seismic information can be used to classify reservoir lithologies and pore fluids. One of the innovations was to use a seismic impedance attribute (related to the VP/VS ratio) that incorporates far‐offset data, but at the same time can be practically obtained using normal incidence inversion algorithms. The methods were applied to a North Sea turbidite system. We incorporated well log measurements with calibration from core data to estimate the near‐offset and far‐offset reflectivity and impedance attributes. Multivariate probability distributions were estimated from the data to identify the attribute clusters and their separability for different facies and fluid saturations. A training data was set up using Monte Carlo simulations based on the well log—derived probability distributions. Fluid substitution by Ga...

Stochastic reservoir characterization using prestack seismic data

Reservoir characterization must be based on information from various sources. Well observations, seismic reflection times, and seismic amplitude versus offset (AVO) attributes are integrated in this study to predict the distribution of the reservoir variables, i.e., facies and fluid filling. The prediction problem is cast in a Bayesian setting. The a priori model includes spatial coupling through Markov random field assumptions and intervariable dependencies through nonlinear relations based on rock physics theory, including Gassmanns relation. The likelihood model relating observations to reservoir variables (including lithology facies and pore fluids) is based on approximations to Zoeppritz equations. The model assumptions are summarized in a Bayesian network illustrating the dependencies between the reservoir variables. The posterior model for the reservoir variables conditioned on the available observations is defined by the a priori and likelihood models. This posterior model is not analytically tra...

Predicting stress-induced velocity anisotropy in rocks

A simple transformation, using measured isotropic VP and VS versus hydrostatic pressure, is presented for predicting stress‐induced seismic velocity anisotropy in rocks. The compliant, crack‐like portions of the pore space are characterized by generalized compressional and shear compliances that are estimated from the isotropic VP and VS. The physical assumption that the compliant porosity is crack‐like means that the pressure dependence of the generalized compliances is governed primarily by normal tractions resolved across cracks and defects. This allows the measured pressure dependence to be mapped from the hydrostatic stress state to any applied nonhydrostatic stress. Predicted P‐ and S‐wave velocities agree reasonably well with uniaxial stress data for Barre Granite and Massillon Sandstone. While it is mechanically similar to methods based on idealized ellipsoidal cracks, the approach is relatively independent of any assumed crack geometry and is not limited to small crack densities.

Seismic pore space compressibility and Gassmann’s relation

The pore space compressibility of a rock provides a robust, model-independent descriptor of porosity and pore fluid effects on effective moduli. The pore space compressibility is also the direct physical link between the dry and fluid-saturated moduli, and is therefore the basis of Gassmanns equation for fluid substitution. For a fixed porosity, an increase in pore space compressibility increases the sensitivity of the modulus to fluid substitution. Two simple techniques, based on pore compressibility, are presented for graphically applying Gassmanns relation for fluid substitution. In the first method, the pore compressibility is simply reweighted with a factor that depends only on the ratio of fluid to mineral bulk modulus. In the second technique, the rock moduli are rescaled using the Reuss average, which again depends only on the fluid and mineral moduli.

Pore fluid effects on seismic velocity in anisotropic rocks

A simple new technique predicts the high‐ and low‐frequency saturated velocities in anisotropic rocks entirely in terms of measurable dry rock properties without the need for idealized crack geometries. Measurements of dry velocity versus pressure and porosity versus pressure contain all of the necessary information for predicting the frequency‐dependent effects of fluid saturation. Furthermore, these measurements automatically incorporate all pore interaction, so there is no limitation to low crack density. The velocities are found to depend on five key interrelated variables: frequency, the distribution of compliant crack‐like porosity, the intrinsic or noncrack anisotropy, fluid viscosity and compressibility, and effective pressure. The sensitivity of velocities to saturation is generally greater at high frequencies than low frequencies. The magnitude of the differences from dry to saturated and from low frequency to high frequency is determined by the compliant or crack‐like porosity. Predictions of s...